Question: Which of the following numbers is a multiple of 5? ${69,83,84,105,116}$
Answer: The multiples of $5$ are $5$ $10$ $15$ $20$ ..... In general, any number that leaves no remainder when divided by $5$ is considered a multiple of $5$ We can start by dividing each of our answer choices by $5$ $69 \div 5 = 13\text{ R }4$ $83 \div 5 = 16\text{ R }3$ $84 \div 5 = 16\text{ R }4$ $105 \div 5 = 21$ $116 \div 5 = 23\text{ R }1$ The only answer choice that leaves no remainder after the division is $105$ $ 21$ $5$ $105$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $105$ $105 = 3\times5\times7 5 = 5$ Therefore the only multiple of $5$ out of our choices is $105$. We can say that $105$ is divisible by $5$.